Soura Dasgupta

Asymptotically convergent modified recursive least-squares with data-dependent updating and forgetting factor for systems with bounded noise

Continual updating of estimates required by most recursive estimation schemes often involves redundant usage of information and may result in system instabilities in the presence of bounded output disturbances. This paper investigates an algorithm which has the capability of eliminating these difficulties. Based on a set theoretic assumption, the algorithm yields modified least-squares estimates with a forgetting factor. It updates the estimates selectively depending on whether the observed data contain sufficient information. The information evaluation required at each step involves very simple computations. In addition, the parameter estimates are shown to converge asymptotically to a region around the true parameter at an exponential rate.

Control of Minimally Persistent Formations in the Plane

This paper studies the problem of controlling the shape of a formation of point agents in the plane. A model is considered where the distance between certain agent pairs is maintained by one of the agents making up the pair; if enough appropriately chosen distances are maintained, with the number growing linearly with the number of agents, then the shape of the formation will be maintained. The detailed question examined in the paper is how one may construct decentralized nonlinear control laws to be operated at each agent that will restore the shape of the formation in the presence of small distortions from the nominal shape. Using the theory of rigid and persistent graphs, the question is answered. As it turns out, a certain submatrix of a matrix known as the rigidity matrix can be proved to have nonzero leading principal minors, which allows the determination of a stabilizing control law.

Control of a three-coleader formation in the plane

This paper considers a formation of three point agents moving in the plane, where the agents have a cyclic ordering with each one required to maintain a nominated distance from its neighbour; further, each agent is allowed to determine its movement strategy using local knowledge only of the direction of its neighbour, and the current and desired distance from its neighbour. The motion of the formation is studied when distances are initially incorrect. A convergence result is established, to the effect that provided agents never become collinear, the correct distances will be approached exponentially fast, and the formation as a whole will rotate by a finite angle and translate by a finite distance.

Source Localization in Wireless Sensor Networks From Signal Time-of-Arrival Measurements

Recent advances in wireless sensor networks have led to renewed interests in the problem of source localization. Source localization has broad range of applications such as emergency rescue, asset inventory, and resource management. Among various measurement models, one important and practical source signal measurement is the received signal time of arrival (TOA) at a group of collaborative wireless sensors. Without time-stamp at the transmitter, in traditional approaches, these received TOA measurements are subtracted pairwise to form time-difference of arrival (TDOA) data for source localization, thereby leading to a 3-dB loss in signal-to-noise ratio (SNR). We take a different approach by directly applying the original measurement model without the subtraction preprocessing. We present two new methods that utilize semidefinite programming (SDP) relaxation for direct source localization. We further address the issue of robust estimation given measurement errors and inaccuracy in the locations of receiving sensors. Our results demonstrate some potential advantages of source localization based on the direct TOA data over time-difference preprocessing.

Conditions for designing strictly positive real transfer functions for adaptive output error identification

Strictly positive real (SPR) transfer functions are of importance in Adaptive systems theory. This paper addresses two issues related to finding a polynomial b(s) such that b(s)/a(s) is SPR for all a(s) belonging to a set of n th-degree Hurwitz polynomials {\P}^n defined by the magnitude bounds on the coefficients of a(s) . It is shown that irrespective of n there exist four polynomials in {\P}^n such that if the ratios of b(s) with each of these is SPR then b(s)/a(s) is SPR for all members of {\P}^n . A sufficient condition for the existence of this b(s) along with a method for its construction is outlined. The condition resembles the Routh array test for determining system stability.

Circumnavigation Using Distance Measurements Under Slow Drift

Consider an agent A at an unknown location, under going sufficiently slow drift, and a mobile agent B that must move to the vicinity of and then circumnavigate A at a prescribed distance from A. In doing so, B can only measure its distance from A, and knows its own position in some reference frame. This paper considers this problem, which has applications to surveillance and orbit maintenance. In many of these applications it is difficult for B to directly sense the location of A, e.g. when all that B can sense is the intensity of a signal emitted by A. This intensity does, however provide a measure of the distance. We propose a nonlinear periodic continuous time control law that achieves the objective using this distance measurement. Fundamentally, a) B must exploit its motion to estimate the location of A, and b) use its best instantaneous estimate of where A resides, to move itself to achieve the circum navigation objective. For a) we use an open loop algorithm formulated by us in an earlier paper. The key challenge tackled in this paper is to design a control law that closes the loop by marrrying the two goals. As long as the initial estimate of the source location is not coincident with the intial position of B, the algorithm is guaranteed to be exponentially convergent when A is stationary. Under the same condition, we establish that when A drifts with a sufficiently small, unknown velocity, B globally achieves its circumnavigation objective, to within a margin proportional to the drift velocity.

Target Tracking and Mobile Sensor Navigation in Wireless Sensor Networks

This work studies the problem of tracking signal-emitting mobile targets using navigated mobile sensors based on signal reception. Since the mobile targets maneuver is unknown, the mobile sensor controller utilizes the measurement collected by a wireless sensor network in terms of the mobile target signals time of arrival (TOA). The mobile sensor controller acquires the TOA measurement information from both the mobile target and the mobile sensor for estimating their locations before directing the mobile sensors movement to follow the target. We propose a min-max approximation approach to estimate the location for tracking which can be efficiently solved via semidefinite programming (SDP) relaxation, and apply a cubic function for mobile sensor navigation. We estimate the location of the mobile sensor and target jointly to improve the tracking accuracy. To further improve the system performance, we propose a weighted tracking algorithm by using the measurement information more efficiently. Our results demonstrate that the proposed algorithm provides good tracking performance and can quickly direct the mobile sensor to follow the mobile target.

Control of Minimally Persistent Leader-Remote-Follower and Coleader Formations in the Plane

This paper solves an n -agent formation shape control problem in the plane. The objective is to design decentralized control laws so that the agents cooperatively restore a prescribed formation shape in the presence of small perturbations from the prescribed shape. We consider two classes of directed, cyclic information architectures associated with so-called minimally persistent formations: leader-remote-follower and coleader. In our framework the formation shape is maintained by controlling certain interagent distances. Only one agent is responsible for maintaining each distance. We propose a decentralized control law where each agent executes its control using only the relative position measurements of agents to which it must maintain its distance. The resulting nonlinear closed-loop system has a manifold of equilibria, which implies that the linearized system is nonhyperbolic. We apply center manifold theory to show local exponential stability of the desired formation shape. The result circumvents the non-compactness of the equilibrium manifold. Choosing stabilizing gains is possible if a certain submatrix of the rigidity matrix has all leading principal minors nonzero, and we show that this condition holds for all minimally persistent leader-remote-follower and coleader formations with generic agent positions. Simulations are provided.

Distributed Control for Optimal Economic Dispatch of a Network of Heterogeneous Power Generators

In this paper, we present a simple, distributed algorithm for frequency control and optimal economic dispatch of power generators. In this algorithm, each generator independently adjusts its power-frequency set-points of generators to correct for generation and load fluctuations using only the aggregate power imbalance in the network, which can be observed by each generator through local measurements of the frequency deviation on the grid. In the absence of power losses, we prove that the distributed algorithm eventually achieves optimality, i.e., minimum cost power allocations, under mild assumptions (strict convexity and positivity of cost functions); we also present numerical results from simulations to compare its performance with traditional (centralized) dispatch algorithms. Furthermore, we show that the performance of the algorithm is robust in the sense that, even with power losses, it corrects for frequency deviations, and, for low levels of losses, it still achieves near-optimal allocations; we present an approximate analysis to quantify the resulting suboptimality.

A Semidefinite Programming Approach to Source Localization in Wireless Sensor Networks

We propose a novel approach to the source localization and tracking problem in wireless sensor networks. By applying minimax approximation and semidefinite relaxation, we transform the traditionally nonlinear and nonconvex problem into convex optimization problems for two different source localization models involving measured distance and received signal strength. Based on the problem transformation, we develop a fast low-complexity semidefinite programming (SDP) algorithm for two different source localization models. Our algorithm can either be used to estimate the source location or be used to initialize the original nonconvex maximum likelihood algorithm.